Need help rendering a panoramic equirectangular movie of a computer game recorded in box projection mode in cycles
It is hard to say for sure without the video file, but based on what you provided the answer is pretty simple: your camera is not actually positioned inside the cube.  It is positioned outside the cube, and therefore it's just rendering the face of the cube that's visible to it.  

I made a few minor changes to your file: I repositioned the camera to inside the cube; rotated it 180 degrees to face the "middle" of the image; played with your cube's UV map to get it to fit the still you provided; and changed the material to an emission shader for visibility.  This was my render:



Is this the type of thing you had in mind?

Edit: since the cockpit still was not posted in the question I am including it here for reference.



with some further tweaking, I got the render to look like this:



It is important that the camera be centered within the cube, you can align the objects by using the Object-->Transform-->Align Objects command.

There are some discontinuities in the image, a few may have to do with my lack of precision in adjusting the UVs, but I think most of them come from the fact that your sample image does not wrap perfectly.  The panel to the top of the center is screwed up somehow, for example it includes additional images of those windshield seams.  Also the seam where the leftmost and rightmost edges join doesn't seem to be a perfect fit.